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Global Convergence of Time-Periodic Negative-Feedback Systems via Monotone Embedding

A criterion guaranteeing that every orbit of a time-periodic closed-loop negative-feedback system converges to a harmonic periodic solution. Students learn how embedding the feedback system into a larger time-periodic monotone dynamical system, and studying the associated Poincare map, yields global convergence, with application to periodically-forced gene regulatory models.

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Global convergence for time-periodic systems with negative feedback and applications

For the discrete-time dynamical system generated by the Poincare map T of a time-periodic closed-loop negative feedback system, we present an amenable condition which enables us to obtain the global …